# Force and laws of motion

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### FORCE AND LAWS OF MOTION:

FORCE AND LAWS OF MOTION CLASS: IX SUBJECT: SCIENCE PREPARED BY : Tushar Joshi

### force:

force Force is an external influence which changes or tends to change the state of rest, speed or direction of an object or shape of an object. It is a vector quantity. S.I. unit is Newton ( N ). The pull or push acting on the body is known as force. Effect of force: It can change the speed of the object. It can increase or decrease the speed or can move or stop the body. It can change the direction of moving object. It can change the shape of the object.

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FORCE CAN MOVE AN OBJECT

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FORCE CAN STOP THE OBJECT

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FORCE CAN CHANGE THE DIRECTION OF AN OBJECT

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FORCE CAN MOVE AN OBJECT

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FORCE CAN CHANGE THE SHAPE OF AN OBJECT

### Types of forces:

Types of forces Balanced force: When two or more forces are acting on an object, and there is no change in the position or state of the object the force is called balanced force. Example: In a tug of war when the two teams pull with equal effort the and the two teams remain stationary. Thus, when the resultant of all the forces acting on a body is zero the force is called balanced force 5 N 5 N Y X The object will not move

BALANCED FORCE

Balanced force

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Unbalanced force: When two or more forces acting on an object in such a way that object moves in the direction of any force acting on it, the force is called unbalanced force. Example: In a tug of war if one team is stronger than the other, the stronger team will pull the weaker one towards their side due to unbalanced force. 5 N 10 N Y X The object will move in this direction

Unbalanced force

Unbalanced force

### Newton’s law of motion:

Newton’s law of motion First law of motion: Newton’s first law of motion states that every body continues in its state of rest or of uniform motion in a straight line unless and until it is compelled by some external force to change its state. Newton’s first law consists of two parts: A body at rest , continues to be in its state of rest unless it is disturbed by some external force. A body in motion continues moving in a straight line with uniform velocity unless some external force is acted upon it.

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Inertia: The tendency of a body to oppose any change in its state of rest or of uniform motion is called inertia of the body. Relationship between mass of the body and inertia: Inertia of a body is directly proportional to the mass of the body. Mass of the body is the measure of inertia. More the mass more the inertia. Types of inertia: Inertia of rest Inertia of motion Inertia of direction

### Inertia of rest:

Inertia of rest The tendency of a body to oppose any change in its state of rest unless an external force acts on it is known as inertia of rest. Illustration: A person sitting in a bus falls backward if the bus suddenly starts. This is because the lower part of the body begins to move along with the bus but upper part tends to remain at rest due to inertia of rest. If a coin is placed on a card covering the mouth of a tumbler and the card is given a sudden jerk the coin will fall into the tumbler. This is because the card comes in motion when we strike it with a finger but the coin remains at rest due to inertia of rest.

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When a branch of a tree is shaken the fruits/leaves get separated due to inertia of rest. The carpet is beaten with stick to remove the dust particles. This is because when the carpet is beaten with the stick, the fibers of the carpet comes in motion and hence move forward but the dust particles remains at rest due to inertia of rest. Water in the form of small droplets fall down when a wet pieces of cloth is shaken. This is because the fibers of the cloth comes in motion but water remains at rest due to inertia of rest.

### Inertia of motion:

Inertia of motion The tendency of a body to oppose any change in its state of uniform motion unless an external force acts on it is called inertia of motion. Illustration: The passengers fall forward when a fast moving bus stops suddenly. This is because the lower part of the body of the passengers come to rest as soon as the bus stop but upper part of their bodies continue to move forward due to inertia of motion. A person falls forward while getting down from a moving train or bus. This is because feet come to rest suddenly but the upper part of his body retains the forward motion due to inertia of motion. An athlete runs a certain distance before taking a leap We remove mud from our shoes by striking them against wall.

### Inertia of direction:

Inertia of direction The tendency of a body to oppose any change in its direction of motion unless an external force act on it is known as inertia of direction. Illustration: Tie a stone to one end of a string and holding other end of the string in hand. Rotate the stone in a horizontal circle. If during rotation the string breaks the stone is found to fly off tangentially at the point of circle. The water drops striking to cycle tyre are found to fly off tangentially.

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Inertia of direction

### Newton’s 2nd law of motion:

Newton’s 2 nd law of motion Newton’s second law of motion states that the force is directly proportional to the product of mass and acceleration. F α ma F = Kma where K is the proportionality constant If K is 1 then F = ma and a = F/m i.e. acceleration produced in a body is directly proportional to the force applied and inversely proportional to the mass of the body.

### Relation between Newton and dyne:

Relation between Newton and dyne F = m x a 1 N = 1 kg x 1 m/s 2 1 N = 1000 g x 100 cm/s 2 1 N = 10 5 g cm/s 2 1 N = 10 5 dyne

### momentum:

momentum It is the quantity of motion contained in a body and is equal to the product of mass and velocity. Momentum = mass x velocity p = mv where p is the momentum of a body m is the mass of the body v is the velocity of the body. If a body is at rest its velocity is zero and so its momentum is also zero. The SI unit of momentum is kilogram meter per second or kg m/s or kg ms -1 E.g. A truck moving at a very low speed can kill a person standing in its path because of the heavy mass of the truck. A bullet of small mass when fired from a gun can kill a person because of the large velocity of the bullet. So the impact of a body depends upon its mass and velocity.

### Newton’s 2nd law in terms of momentum:

Newton’s 2 nd law in terms of momentum It states that the rate of change of momentum of an object is proportional to the applied force in the direction of force. Mathematical formulation of Second law of motion: If an object of mass m is moving along a straight line with initial velocity u and is accelerated to velocity v in time t by applying a force F, then Initial momentum p 1 = mu Final momentum p 2 = mv

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Change in momentum p 2 – p 1 = mv – mu = m (v – u ) Rate of change of momentum =m (v – u )/t Or, the applied force F α m (v – u )/t Or, F = km (v – u )/t but (v – u )/t = a So, F = kma where k is a constant of proportionality Or, F = ma

### Impulse:

Impulse Impulse is defined as he product of the force and time for which it act and is equal to the total change in momentum. It is a vector quantity. S.I. unit is Newton second (Ns) Impulse = Force x Time = F x t Since F = ma = m ( v – u )/t Or, Ft = m ( v – u ) Or, Ft = mv – mu Therefore Impulse = total change in momentum

### Newton’s third law of motion :

Newton’s third law of motion Newton’s third law of motion states that ‘To every action there is an equal and opposite reaction and they act on two different bodies.’ Illustrations: Take two spring balances A and B connected together. Fix the spring balance B to a rigid support. When a force is applied by pulling the free end of the spring balance A, both the spring balances show the same readings. This shows that the force exerted by the spring balance A on B is equal but opposite in direction to the force exerted by spring balance B on A. The force exerted by the spring balance A on B is action and the force exerted by the spring balance B on A is reaction.

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Examples: While swimming a man pushes the water backward with hands. The reaction offered by water to man pushes him forward. Recoiling of gun/rifle/piston. When a ball is dropped from some height it rebounds after striking against a floor. A book lying on the table exerts upon it a downward force ( action ) equal to the weight of the body. The table exerts an equal and opposite force ( reaction ) on the book. This make the book to remain in equilibrium.

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Third law of motion

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Newton’s 3 rd law

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Recoil force on the gun Accelerating force on the bullet Action Reaction When a bullet is fired from a gun, it exerts a forward force (action) on the bullet and the bullet exerts an equal and opposite force on the gun (reaction) and the gun recoils.

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When a sailor jumps out of a boat, he exerts a backward force of the boat (action) and the boat exerts an equal and opposite force on the sailor (reaction) and the sailor jumps forward.

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When a rocket is fired, the force of the burning gases coming out (action) exerts an equal and opposite force on the rocket (reaction) and it moves upward.

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When an air filled balloon is released, the force of the air coming out of the balloon (action) exerts an equal and opposite force on the balloon (reaction) and it moves upward.

### Law of conservation of momentum:

Law of conservation of momentum According to this law, the total momentum of a system or a body remain constant if no net external force acts on the system. Since F = P 2 – P 1 /t Or, Ft = P 2 – P 1 If F = 0 then P 1 = P 2

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Illustration for law of conservation of momentum: uA uB FAB Before collision FBA vA vB After collision MA MA MB B A MB

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Let two ball A and B of mass MA and MB travelling in the same direction along a straight line at different velocities uA and uB respectively. There is no external force acts on them. Let uA is greater than uB and the two balls collide with each other. During collision which last for time ‘t’ , the ball A exerts a force AB on ball B and the ball B exerts a force BA on the ball A . Suppose vA and vB are velocities of the two ball A and B after collision respectively. Since P = mv Therefore the momentum of ball A before and after collision are mAuA and mAvA respectively. Similarly the momentum of ball B before and after collision are mBuB and mBvB respectively.

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Therefore the rate of change of momentum of ball A = mA(vA–uA)/t and the rate of change of momentum of ball B = mB(vB-uB)/t According to third law of motion the force FAB exerted by ball A on ball B ( action ) is equal to the force FBA exerted by the ball B on the ball A ( reaction ). Therefore FAB = -FBA Or, mA(vA-uA)/t = -mB(vB-uB)/t Or, mAvA - mAuA = -mBvB + mBuB Or, -mAuA – mBuB = -mAvA – mBvB Or, mAuA + mBuB = mAvA + mBvB Since (mAuA+mBuB) is the total momentum of two balls A & B before collision and (mAvA+mBvB) is the total momentum after collision. Then total momentum of the two balls remain unchanged or conserved when no external force is applied. 